Theory of Investments

writen by Trygwe Haavelmo
About autor:

The Norwegian economist Trygve Haavelmo began his career as a student of Ragnar Frisch at University of Oslo.  He went to the United States  in 1939 as a Fulbright scholar, where he ended up staying until 1947.  Haavelmo spent much of his sojourn at the Cowles Commission, before returning to Oslo.  He remained a professor a the University of Oslo until his retirement. Trygve Haavelmo won the Nobel memorial prize in 1989.

It was during his stay in the United States that Haavelmo wrote his most influential work -- a 1944 article introducing the "probability approach" to econometrics. The "probability" approach argued that we should envision existing economic data series as being "a sample selected by Nature", i.e. randomly derived from a "hypothetical" series of distribution which governed reality but which was unobservable. Thus, Haavelmo argued, we can test the validity of economic theories by couching the theoretical model in terms of statistical relationships which can then be tested. The relationship between theory and the hypothetical underlying "reality", argued Haavelmo, is akin to the relationship between the observed data and that "reality". Therefore, if we can come close in relating theory with observed data in some precisely defined statistical manner, then we are effectively saying we have "reproduced" another "natural drawing" from the hypothetical "reality" and thus our theoretical relationships are in a sense "true".

Haavelmo also addressed the issues of identification problems in simultaneous equations econometric problems (Haavelmo, 1943, 1947).  It was Haavelmo who differentiated the "structural" from the "reduced" form equation and discussed the relationship between the original parameters and the reduced-form estimates.  It was Haavelmo that introduced the "determinant condition" for identifiability.   This set the ground for the "Cowles approach" approach to econometrics and the methodological debates on empirical economics that raged during the 1940s.

Theory of investments:

If only we knew more about the determinants of investment! But, unfortunately, our knowledge in this direction is still very meager. One might well ask, What is wrong with the theory of investment? Or, perhaps, What is wrong with the subject matter itself! For one thing, this variable, -- the pivot of modern macroeconomics -- has apparently lived a somewhat nomadic life among the various chapters of economic theory. Perhaps it has not stayed long enough in any one place. Perhaps it has been ill-treated. What is investment? Strictly speaking, investment is the change in capital stock during a period. Consequently, unlike capital, investment is a flow term and not a stock term. This means that while capital is measured at a point in time, while investment can only be measured over a period of time. If we ask "what is capital right now?", we might get an answer along the lines of $10 trillion. But if we ask "what is investment right now?", this cannot be answered. The quantity of a flow always depends on the period in consideration. Thus, we can answer "what is investment this month?" (and might be told it is $10 million) or "what is investment this year?" (and might be told $1 billion).

We can calculate the investment flow in a period as the difference between the capital stock at the end of the period and the capital stock at the beginning of the period. Thus, the investment flow at time period t can be defined as:

It = Kt - Kt-1

where Kt is the stock of capital at the end of period t and Kt-1 is the stock of capital at the end of period t-1 (and thus at the beginning of period t).

Personal finance and loans

How is the the theory of investment different from the theory of capital? If all capital is circulating capital, so that it is completely used up within a period, then no capital built up during the previous period can be brought over into next period. In this special case, the theory of capital and the theory of investment become one and the same thing.

With fixed capital, the story is different -- and more complicated as there seems to be two decisions that must be addressed: the amount of capital and the amount of investment. These are different decisions. One is about the desired level of capital stock. The other is about the desired rate of investment flow. The decisions governing one will inevitably affect the other, but it is not necessarily the case that one is reducible to the other.

There are effectively two ways of thinking about investment. At the risk of annoying some people, we shall refer to these as the "Hayekian" and "Keynesian" perspectives. The Hayekian perspective conceives of investment as the adjustment to equilibrium and thus the optimal amount of investment is effectively a decision on the optimal speed of adjustment. A firm may decide it needs a factory (the "capital stock" decision), but its decision on how fast to build it, how much to spend each month building it, etc. -- effectively, the "investment" decision -- is a separate consideration.

Naturally, the capital decision influences the investment decision: a firm which has $10 billion of capital and decides that it needs $15 billion of capital, therefore requires investment of $5 billion. But if this adjustment can be done "instantly", then there is really no actual investment decision to speak of. We just change the capital stock automatically. The capital decision governs everything.

However, if for some reason, instant adjustment is not possible, then the investment story begins to matter. How do we distribute this $5 billion adjustment? Do we invest in an even flow over time, e.g. $1 billion this week, another $1 billion next week, and so on? Or do we invest in descending increments, e.g. invest $1 billion this week, $500 million next week, $300 million the week after that, etc. and approach the $5 billion mark asymptotically? Or should we invest in ascending increments, e.g. $10 million this week, $100 million next week, etc.? Delivery costs, changing prices of suppliers, fluctuating interest rates and financing costs, and other such considerations, make some adjustment processes more desirable than others. These different patterns of "approaching" the desired $5 billion adjustment in capital stock and the considerations that enter into determining which adjustment pattern to follow is what lies at the heart of the Hayekian approach to investment theory.

The Hayekian approach is shown heuristically in Figure 1, where we start at capital stock K0 and then, at t*, we suddenly change our desired capital stock from K0 to K*. Figure 1 depicts four alternative investment paths from K0 towards K*. Path I represents "instant" adjustment type of investment (i.e. all investment happens at once at t* and no more investment afterwards). Path I˘ represents an "even flow" adjustment path, with investment happening at a steady rate after t* until K* is reached. Path I˘ ˘ is the asymptotic investment path (gradually declining investment), while path I˘ ˘ ˘ depicts a gradually increasing investment path. All paths, except for the first instant one, imply that "investment" flows will be happening during the periods that follow t*. Properly speaking, then, investment theory in the Hayekian perspective is concerned with analyzing and comparing paths such as I˘ , I˘ ˘ and I˘ ˘ ˘ .

 invest1.gif (3312 bytes)

Figure 1 - Adjustment Paths towards K*

The "Keynesian" approach places far less emphasis on the "adjustment" nature of investment. Instead, they have a more "behavioral" take on the investment decision. Namely, the Keynesian approach argues that investment is simply what capitalists "do". Every period, workers consume and capitalists "invest" as a matter of course. This leads Keynesians to underplay the capital stock decision. This does not mean that Keynesians ignore the fact that investment is defined as a change in capital stock. Rather, they believe that the main decision is the investment decision; the capital stock just "follows" from the investment patterns rather than being an important thing that needs to be "optimally" decided upon beforehand. Thus, when businesses make investment decisions, they do not have an "optimal capital stock" in the back of their mind. They are more concerned as to what is the optimal amount of investment for some particular period. For Keynesians, then, optimal investment not about "optimal adjustment" but rather about "optimal behavior".


Major Works of Trygve Haavelmo

  • "The Method of Supplementary Confluent Relations", 1938, Econometrica
  • "The Inadequacy of Testing Dynamic Theory by Comparing the Theoretical Solutions and Observed Cycles", 1940, Econometrica
  • "Statistical Testing of Business Cycles", 1943, RES
  • "The Statistical Implications of a System of Simultaneous Equations", 1943, Econometrica
  • "The Probability Approach in Econometrics", 1944, Econometrica
  • "Multiplier Effects of a Balanced Budget", 1945, Econometrica ("Supp. Notes", 1946)
  • "Family Expenditures and the Marginal Propensity to Consume", 1947, Econometrica
  • "Methods of Measuring the Marginal Propensity to Consume", 1947, JASA
  • "A Note on the Theory of Investment", 1950, RES
  • "The Concepts of Modern Theories of Inflation", 1951, Eknomisk Tidssk
  • A Study in the Theory of Economic Evolution, 1954.
  • "The Role of the Econometrician in the Advancement of Economic Theory", 1958, Econometrica
  • A Study in the Theory of Investment, 1960.
  • "Business Cycles II: Mathematical ", 1968, IESS
  • Variation on a Theme by Gossen, 1972 (Swedish)
  • "What Can Static Equilibrium models Tell Us?", 1974, Econ Inquiry
  • "Econometrics and the Welfare State", 1990, Les Prix Nobel de 1989


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